SarkariPYQ

SSC CPO 2022 PYQ — Question 111

SSC CPO - 11 Nov 2022 - Shift 3 • Quantitative Aptitude • Q111

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Simplify.

cos4θ−sin4θsin2θ{cos^4\theta- sin^4\theta\over sin^2\theta}

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Correct answer: C

Explanation

The correct answer is option 3 i.e. cot2θ−1cot^2\theta-1

Given that

 Simplify.

cos4θ−sin4θsin2θ{cos^4\theta- sin^4\theta\over sin^2\theta}

⇒ cos4θ−sin4θsin2θ{cos^4\theta- sin^4\theta\over sin^2\theta}

⇒ (cos2θ−sin2θ)(cos2θ+sin2θ)sin2θ{(cos^2\theta- sin^2\theta)(cos^2\theta+sin^2\theta)\over sin^2\theta}

⇒ (cos2θ−sin2θ)(cot2θ+1){(cos^2\theta- sin^2\theta)(cot^2\theta+1)}

⇒ (cos2θ−sin2θ)(cosec2θ){(cos^2\theta- sin^2\theta)(cosec^2\theta)}

⇒ cot2θ−1cot^2\theta-1